Question

Find the length of each chord. horizontal chord and vertical

Answer 1

Consider the circle

we have the intersecting chords theorem, which states that

`a\cdot b=c\cdot d`

In our case we have a=x, b=12, c=6 and d=x+4. So we have

`12\cdot x=6\cdot(x+4)`

distributing on the right side we get

`12\cdot x=6x+6\cdot4=6x+24`

Subtracting 6x on both sides, we get

`24=12x\text{ -6x=6x}`

Dividing boht sides by 6, we get

`x=(24)/(6)=4`

So, the value of x is 4. Now we replace this value to find the length of each chord, so we have

x---->4

12---->12

x+4----->4+4=8

6----->6